Nodal solutions for Kirchhoff equation in R3 with critical growth. (April 2020)

• Record Type: Journal Article
• Authors: Zhao, Junfang; Liu, Xiangqing
• Is Part Of: Applied mathematics letters. Volume 102(2020)
• Publication Date: 2020-04
• Subjects: Kirchhoff equation -- Nodal solutions -- Critical growth; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106101
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we consider the following Kirchhoff equation in R 3 with critical growth. ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u − V ( x ) u + u 5 + μ | u | q − 2 u = 0, in R 3, u ( x ) → 0, as | x | → ∞, where V is the potential function, a, b, μ > 0, 5 < q < 6 are constants. We assume V is a radial function and is bounded from below by a positive constant. We prove that for any given positive integer k, the problem has a radial solution, having k nodal domains exactly.